Constellation pattern recognition is an important technique that has been used in digital image processing, digital signal processing, and digital communications. It is a statistical technique for recovering a constellation pattern from noisy data inputs by matching the noisy inputs against known alphabet sets. A two-dimensional image or a communication data symbol can be represented by a complex number, and a set of those complex numbers can form a two-dimensional pattern. These two-dimensional patterns include the binary phase-shift-keying, quadrature phase-shift-keying, and 16-ary quadrature-amplitude-modulation constellation patterns depicted in FIGS. 1A-1C. The FIGS. 1A-1C constellation patterns are plotted using an in-phase coordinator for real numbers and a quadrature coordinator for imaginary numbers.
FIG. 1A depicts a binary phase-shift-keying (BPSK) constellation pattern, which has 2 alphabets evenly distributed on a circle. FIG. 1B depicts a quadrature phase-shift-keying (QPSK) constellation pattern with four alphabets evenly distributed on a circle. FIG. 1C is a 16-ary quadrature-amplitude-modulation (QAM) constellation pattern with 16 alphabets evenly distributed on a square. The average power of the constellation alphabets are normalized to one.
Constellation pattern recognition is a statistical method to recover a constellation pattern from noisy data inputs by matching the noisy data inputs to known alphabet sets. Assume that there are L number of constellation pattern candidates and that the ith (i=1, 2, . . . , L) pattern candidate has Mi constellation alphabets denoted by complex numbers {b1(i), b2(i), . . . , bMi(i)}. A number of prior art statistical classification techniques have been developed, such as the Average Likelihood Ratio Test, Generalized Likelihood Ratio Test, Hybrid Likelihood Ratio Test, and higher order techniques.
One widely used statistical classifier used in prior art constellation pattern recognition is the Average Likelihood Ratio Test (ALRT). The ALRT statistical classifier recognizes the unknown constellation pattern by maximizing the logarithmic probability density functions as follows:
                                          l            a                    ⁡                      (                                          H                i                            |                              r                ⁡                                  (                  k                  )                                                      )                          =                              ∑                          k              =              1                        K                    ⁢                      log            ⁢                          {                              p                ⁡                                  (                                                            H                      i                                        |                                          r                      ⁡                                              (                        k                        )                                                                              )                                            }                                                          (        1        )            under the hypothesis that Hi, i=1, 2, . . . , L for L number of constellation pattern candidates, where
                              p          ⁡                      (                                          H                i                            |                              r                ⁡                                  (                  k                  )                                                      )                          =                              1                          M              i                                ⁢                                    ∑                              j                =                1                                            M                i                                      ⁢                          exp              ⁢                              {                                  -                                                                                                                                                                  r                            ⁡                                                          (                              k                              )                                                                                -                                                      b                            j                                                          (                              i                              )                                                                                                                                                  2                                                              2                      ⁢                                              σ                        2                                                                                            }                                                                        (        2        )            is the probability density of the unknown random variable r(k) averaged over Mi alphabets at the instance k. Therefore, the ith constellation pattern will be chosen if the ith test function la(Hi|r(k)) is a maximum. In other words, the noisy input is classified to have the constellation pattern match the ith hypothetical pattern. The other two well known likelihood ratio test methods are Generalized Likelihood Ratio Test (GLRT) and Hybrid Likelihood Ration Test (HLRT). For the GLRT, the noisy data inputs are considered deterministic and unknown, and the maximum likelihood test is used for classification. This method generally yields easier to implement classifiers than the ALRT but it suffers from the nesting problem, which can lead to a failure in uniquely classifying nested patterns.
Under the HLRT technique, the classification is accomplished by combining ALRT and GLRT together. This method avoids the nested constellation problem in GLRT but it can be complicated due to the multi-dimensional maximization required. Higher-order cyclic stationary and higher-order cumulants were also used for classifying the constellations of the communication signals. However, those methods usually require a large amount of data for the statistical analysis and are very computationally expensive.
While the prior art ALRT system has performed many valuable functions, it is still beset by a number of difficulties and shortcomings related to its multiple exponential and logarithmic calculations. These ALRT calculations are very computation intensive, tedious, and extremely time-consuming. In fact, current ALRT systems are so computation-intensive, tedious, and time-consuming that they are not feasible for real-time recognition operations in the adaptive demodulation of software radio. Currently, the modulation classification is conducted by taking snapshots of the data. Since the content of the data is of interest, the classification processing can be performed in between two snapshots which is usually a large time interval. While in the adaptive demodulation case, the classification is performed to the signal, one block after another. The classification processing of the current block has to be done promptly in a very short time interval before the next block comes. Thus, there has been a long-felt need for faster modulation classification processing to satisfy the quality of service in real-time software radio communication applications that has not been met by prior art constellation pattern recognition systems.
Up until now, the long-felt needs for simplified and more rapid constellation pattern recognition systems have not been met.